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<b>thus </b><a NAME="E1:24_1_1"/>
( <font color="Maroon" title="c1">F</font> is <a href="pencil_1.html#V12" title="PENCIL_1:attr.12">non-void-yielding</a> implies for <font color="Olive" title="b1">i</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Olive" title="b1">i</font> is  non <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a>  )
 <b>by </b><i><a class="ref" href="pencil_1.html#D13" target="_self" title="PENCIL_1:def.13">Def13</a>, <a class="ref" href="pencil_1.html#D14" target="_self" title="PENCIL_1:def.14">Def14</a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( ( for <font color="Olive" title="b1">i</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Olive" title="b1">i</font> is  non <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a>  ) implies <font color="Maroon" title="c1">F</font> is <a href="pencil_1.html#V12" title="PENCIL_1:attr.12">non-void-yielding</a> )</span><br/>

<b>assume </b><a NAME="E2:24_1_1"/><i><font color="Green" title="E23">A1</font></i>: 
for <font color="Olive" title="b1">i</font> being   <a href="hidden.html#M1" title="HIDDEN:mode.1">set</a>   st <font color="Olive" title="b1">i</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#K2" title="RELAT_1:func.2">rng</a> <font color="Maroon" title="c1">F</font> holds <br/><font color="Olive" title="b1">i</font> is  non <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a>  <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> 
 ; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> <font color="Maroon" title="c1">F</font> is <a href="pencil_1.html#V12" title="PENCIL_1:attr.12">non-void-yielding</a></span><br/>

<b>let </b><font color="Maroon" title="c2">S</font> be    <a href="pre_topc.html#L1" title="PRE_TOPC:struct.1">TopStruct</a> ; <i><font color="Red">:: according to </font></i><a class="ref" href="pencil_1.html#D14" target="_self" title="PENCIL_1:def.14">PENCIL_1:def 14</a> <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> ( <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c1">F</font> implies  not <font color="Maroon" title="c2">S</font> is <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a> )</span><br/>

<b>thus </b><a NAME="E3:24_1_1"/>
( <font color="Maroon" title="c2">S</font> <a href="hidden.html#R2" title="HIDDEN:pred.2">in</a>  <a href="relat_1.html#NK4" title="RELAT_1:NK.4">rng</a> <font color="Maroon" title="c1">F</font> implies  not <font color="Maroon" title="c2">S</font> is <a href="pencil_1.html#V3" title="PENCIL_1:attr.3">void</a> )
 <b>by </b><i><a class="txt" href="#E2:24_1_1"><i><font color="Green" title="E23">A1</font></i></a></i>; <a class="txt" onclick="hs(this)" href="javascript:()"><i><font color="Red">::  thesis: </font></i></a><span class="hide"> verum</span><br/>


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